• Title/Summary/Keyword: finite difference method

### ANALYSIS OF A ONE-DIMENSIONAL FIN USING THE ANALYTIC METHOD AND THE FINITE DIFFERENCE METHOD

• Han, Young-Min;Cho, Joo-Suk;Kang, Hyung-Suk
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.91-98
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• 2005
• The straight rectangular fin is analyzed using the one-dimensional analytic method and the finite difference method. For the finite difference method, the numbers of nodes vary from 20 to 100. The relative errors of heat loss and temperature between the analytic method and the finite difference method are represented as a function of Biot Number and dimensionless fin length. One of the results shows that the relative error between the analytic method and the finite difference method decreases as the numbers of nodes for finite difference method increase.

### Efficient 3D Acoustic Wave Propagation Modeling using a Cell-based Finite Difference Method (셀 기반 유한 차분법을 이용한 효율적인 3차원 음향파 파동 전파 모델링)

• Park, Byeonggyeong;Ha, Wansoo
• Geophysics and Geophysical Exploration
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• v.22 no.2
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• pp.56-61
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• 2019
• In this paper, we studied efficient modeling strategies when we simulate the 3D time-domain acoustic wave propagation using a cell-based finite difference method which can handle the variations of both P-wave velocity and density. The standard finite difference method assigns physical properties such as velocities of elastic waves and density to grid points; on the other hand, the cell-based finite difference method assigns physical properties to cells between grid points. The cell-based finite difference method uses average physical properties of adjacent cells to calculate the finite difference equation centered at a grid point. This feature increases the computational cost of the cell-based finite difference method compared to the standard finite different method. In this study, we used additional memory to mitigate the computational overburden and thus reduced the calculation time by more than 30 %. Furthermore, we were able to enhance the performance of the modeling on several media with limited density variations by using the cell-based and standard finite difference methods together.

### FRACTIONAL CHEBYSHEV FINITE DIFFERENCE METHOD FOR SOLVING THE FRACTIONAL BVPS

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.299-309
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• 2013
• In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

### Time-Dependent Optimal Heater Control Using Finite Difference Method

• Li, Zhen-Zhe;Heo, Kwang-Su;Choi, Jun-Hoo;Seol, Seoung-Yun
• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2254-2255
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• 2008
• Thermoforming is one of the most versatile and economical process to produce polymer products. The drawback of thermoforming is difficult to control thickness of final products. Temperature distribution affects the thickness distribution of final products, but temperature difference between surface and center of sheet is difficult to decrease because of low thermal conductivity of ABS material. In order to decrease temperature difference between surface and center, heating profile must be expressed as exponential function form. In this study, Finite Difference Method was used to find out the coefficients of optimal heating profiles. Through investigation, the optimal results using Finite Difference Method show that temperature difference between surface and center of sheet can be remarkably minimized with satisfying Temperature of Forming Window.

### Numerical Analysis of Laminar Natural Convection Heat Transfer around Two Vertical Fins by a Spectral Finite Difference Method

• Haehwan SONG;MOCHIMARU Yoshihiro
• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.56-57
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• 2003
• A numerical solution is presented for the natural convection heat transfer from two vertical fins using a spectral finite difference method. Virtual distant boundary conditions for two bodies that are compatible with plume behavior and with an overall continuity condition are introduced. A boundary-fitted coordinate system is formed. Streamlines, isotherms, mean Nusselt numbers and drag & lift coefficients are presented for a variety of dimensionless parameters such as a Grashof number and a Prandtl number at a steady-state. Extensive effectiveness of a spectral finite difference method was established.

### A Comparison between 3-D Analytical and Finite Difference Method for a Trapezoidal Profile Fin

• Lee, Sung-Joo;Kang, Hyung-Suk
• Journal of Industrial Technology
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• v.21 no.A
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• pp.41-50
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• 2001
• A comparison is made of the temperature distribution and heat loss from a trapezoidal profile fin using two different 3-dimensional methods. These two methods are analytical and finite difference methods. In the finite difference method 78 nodes are used for a fourth of the fin. A trapezoidal profile fin being the height of the fin tip is half of that of the fin base is chosen arbitrarily as the model. One of the results shows that the relative error in the total convection heat loss obtained by using 78 nodes in the finite difference method as compared to the heat conduction through the fin root obtained by analytic method seems to be good (i.e., -3.5%

### A Generalized Finite Difference Method for Solving Fokker-Planck-Kolmogorov Equations

• Zhao, Li;Yun, Gun Jin
• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.816-826
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• 2017
• In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

### Finite Difference Method on Consolidation under Time Dependent Loading (점증하중에 의한 압밀의 유한차분해석)

• Lee, Seung-Hyun
• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.4
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• pp.1895-1899
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• 2012
• Formulation of finite difference method for analyzing consolidation were carried out. It can be seen that the differences in settlement with time obtained by FDM and Terzaghi method are diminished by fine discretization of time increment. Excess pore pressures predicted by the derived finite difference equation were same as those calculated by Olson's method. Predicted time-settlement behavior from the derived finite difference method were almost same as those calculated by Terzaghi's method and Olson's method. Analysis results obtained from the assumed multi-step time dependent loading are thought to be reasonable.

### 2-D Consolidation Numerical Analysis of Multi＿Layered Soils (다층 지반의 2차원 압밀 수치해석)

• 김팔규;류권일;남상규;이재식
• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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• pp.467-474
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• 2000
• The application of Terzaghi's theory of consolidation for analysing the settlement of multi-layered soils is not strictly valid because the theory involves an assumption that the soil is homogeneous. The settlement of stratified soils with confined aquifer can be analysed using numerical techniques whereby the governing differential equation is replaced by 2-dimensional finite difference approximations. The problems of discontinuous layer interface are very important in the algorithm and programming for the analysis of multi-layered consolidation using a numerical analysis, finite difference method(F.D.M.). Better results can be obtained by the process for discontinuous layer interface, since it can help consolidation analysis to model the actual ground The purpose of this paper provides an efficient computer algorithm based on numerical analysis using finite difference method(F.D.M) which account for multi-layered soils with confined aquifer to determine the degree of consolidation and excess pore pressures relative to time and positions more realistically.

### Iterative Analysis for Nonlinear Laminated Rectangular Plates by Finite Difference Method

• Kim, Chi Kyung
• International Journal of Safety
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• v.1 no.1
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• pp.13-17
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• 2002
• A new system of equations governing the nonlinear thin laminated plates with large deflections using von Karman equations is derived. The effects of transverse shear in the thin interlayer are included as part of the analysis. The finite difference method is used to perform the geometrically nonlinear behavior of the plate. The resultant equations permit the analysis of the effect of transverse shear stress deformation on the overall behavior of the interlayer using the load incremental method. For the purpose of feasibility and validity of this present method, the numerical results are compared with other available solutions for accuracy as well as efficiency. The solution techniques have been implemented and the numerical results of example problem are discussed and evaluated.